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The dynamical stresses produced in a thick plate by the action of surface forces

Published online by Cambridge University Press:  18 May 2009

J. Fulton  and
I. N. Sneddon
J. Fulton
Affiliation:
Department of Technical Mathematics, The University, Edinburgh
I. N. Sneddon
Affiliation:
Department of Mathematics, The University, Glasgow
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The first discussion of the propagation of elastic waves in a thick plate was given by Lamb [1] for the two-dimensional problem of a harmonic wave travelling in a direction parallel to the medial plane of the plate. Lamb derived equations relating the thickness of the plate to the phase velocities of two types of wave, one symmetric with respect to the medial plane and the other antisymmetric. The symmetric modes of propagation introduced by Lamb have been studied by Holden [2] and the antisymmetric modes have been studied by Osborne and Hart [3]. More recently Pursey [4] has shown how the amplitude of the disturbance is related to a given distribution of stress, varying harmonically with time, applied to the free surfaces of the plate; two types of source are considered by Pursey, one producing a two-dimensional field of the Lamb type, and the other having circular symmetry about an axis normal to the surface of the plate.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 3 , Issue 4 , July 1958 , pp. 153 - 163
Copyright
Copyright © Glasgow Mathematical Journal Trust 1958

References

REFERENCES

Lamb, H., On waves in an elastic plate, Proc. Roy. Soc. A, 93 (1917), 114–128.Google Scholar
Holden, A. N., Longitudinal modes of elastic waves in isotropic cylinders and slabs, Bell System Tech. Journ., 30 (1951), 956–969.CrossRefGoogle Scholar
Osborne, M. F. M., and Hart, S. D., Transmission, reflection and guiding of an exponential pulse by a steel plate in water, J. Acoust. Soc. Amer., 17 (1945), 1–18.CrossRefGoogle Scholar
Pursey, H., The launching and propagation of elastic waves in plates, Quart. Journ. Mech. and Applied Maths., 10 (1957), 45–62.CrossRefGoogle Scholar
Sneddon, I. N., Quelques solutions des equations du mouvement d'un solide elastique, Rend. Circolo Mat. Palermo, (ii) 3 (1952), 115–129.CrossRefGoogle Scholar
Eason, G., Fulton, J., and Sneddon, I. N., The generation of waves in an infinite elastic solid by variable body forces, Phil. Trans. Roy. Soc. A, 248 (1956), 575–607.Google Scholar
Sneddon, I. N., Fourier Transforms, New York, McGraw–Hill Co., 1951.Google Scholar
Filon, L. N. G., On a quadrature formula for trigonometric integrals, Proc. Roy. Soc., Edinburgh, 49 (1928–9), 38–47.Google Scholar